The question consists of three statements numbered  “I, II and III” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. A man invested Rs. ‘P’ at compound interest of ‘r%’ p.a., compounding annually, in a fixed deposit account. If the amount in the account at the end of 3 years is Rs. 25,000, then find the value of ‘P’.
Assume that the account is used for no other purpose and there was no amount in the account before the investment of Rs. P. Statement I: Balance in the account at the end of two years was Rs. 20,000. Statement II: Difference between interest earned during 2nd year and 3rd year is Rs. 1,000. Statement III: If instead Rs. ‘P’ was invested at simple interest of (1.6r)% p.a., then the interest earned at the end of 3 years would have been more than the actual interest earned.

Statement I: According to the statement; Balance in the account at the end of two years = Rs. 20,000 Balance in the account at the end of three years = Rs. 25,000 So, P × {1 + (r/100)}² = 20000 --------- (I) And, P × {1 + (r/100)}³ = 25000 --------- (II) On dividing equation (II) by equation (I), we have; {1 + (r/100)} = 25000/20000 Or, {1 + (r/100)} = 5/4 Or, {1 + (r/100)} = 1.25 So, r = 25 So, rate of interest = 25% p.a. On putting r = 25 in equation (I), we have; P × (1.25)² = 20000 Or, P × 1.5625 = 20000 Or, P = 12800 So, data in statement I alone is sufficient to answer the question. Statement II: Let {1 + (r/100)} be x. Therefore, Amount at the end of 3 years = Px³ = 25000 Interest earned during 2nd year = Px² - Px Interest earned during 3rd year = Px³ - Px² According to the statement; (Px³ - Px²) - (Px² - Px) = 1000 Or, Px³ - 2Px² + Px = 1000 Since, Px³ = 25000 So, 25000 - 2Px² + Px = 1000 Or, 2Px² - Px = 24000 Dividing throughout by Px³, we get (2x - 1)/x² = 24000/25000 Or, (2x - 1)/x² = 24/25 Or, 24x² - 50x + 25 = 0 Or, 24x² - 30x - 20x + 25 = 0 Or, 6x(4x - 5) - 5(4x - 5) = 0 Or, (4x - 5)(6x - 5) = 0 Or, x = 5/4, 5/6 Since, at x = 5/6, rate will be negative therefore, x = 5/4 Or, {1 + (r/100)} = 5/4 = 1.25 Or, r/100 = 0.25 Or, r = 25 Since, P{1 + (r/100)}³ = 25000 Or, P{1 + (25/100)}³ = 25000 Or, P × (1.25)³ = 25000 Or, 1.953125P = 25000 Or, P = 12800 So, data in statement II alone is sufficient to answer the question. Statement III: According to the statement; If Rs. P was invested at simple interest of (1.6r)% p.a., then interest earned at the end of 3 years would have been more than the actual interest earned. But from this statement, we cannot determine the exact value of r or P. So, data in statement III alone is not sufficient to answer the question. So, data given either in statement I alone or in statement II alone is sufficient to answer the question while data given in statement III alone is not sufficient to answer the question.